On the Perturbative Stability of Quantum Field Theories in de Sitter Space

TL;DR

This paper investigates the stability of the Bunch-Davies vacuum in de Sitter space using a generalized Wigner-Weisskopf method, revealing conditions under which the vacuum decays or remains stable, with implications for particle production and entanglement.

Contribution

It introduces a field theoretic approach to analyze vacuum stability in de Sitter space, identifying decay mechanisms and a non-perturbative screening effect that leads to a stationary vacuum.

Findings

Vacuum does not decay in λφ^4 theory.

Vacuum decay occurs in non-conformally invariant models.

A self-consistent screening mechanism stabilizes the vacuum asymptotically.

Abstract

We use a field theoretic generalization of the Wigner-Weisskopf method to study the stability of the Bunch-Davies vacuum state for a massless, conformally coupled interacting test field in de Sitter space. We find that in $\lambda \phi^4$ theory the vacuum does {\em not} decay, while in non-conformally invariant models, the vacuum decays as a consequence of a vacuum wave function renormalization that depends \emph{singularly} on (conformal) time and is proportional to the spatial volume. In a particular regularization scheme the vacuum wave function renormalization is the same as in Minkowski spacetime, but in terms of the \emph{physical volume}, which leads to an interpretation of the decay. A simple example of the impact of vacuum decay upon a non-gaussian correlation is discussed. Single particle excitations also decay into two particle states, leading to particle production that hastens the exiting of modes from the de Sitter horizon resulting in the production of \emph{entangled superhorizon pairs} with a population consistent with unitary evolution. We find a non-perturbative, self-consistent "screening" mechanism that shuts off vacuum decay asymptotically, leading to a stationary vacuum state in a manner not unlike the approach to a fixed point in the space of states.